13. Find the equations of the bisectors of the sides of the triangle, the equations of whose sides are y — 3x = 1, 39 — 2x = 1, Y — 7x = 0.

14. Find the area of the quadrilateral the equations of whose sides are x + y = 4, 2y — 3x = 5, 12x + 7y = − 35, 4x — 5y = 25.

15. Find the equation of the circle which touches the three lines, x + 2y = 5, 2x + y = 7, y = x + I.

16. Solve the equation

x3 + px1 + qx3 + qx2 + px + I = 0.

17. Find the values of x, y, and z from the equations

sin s

n = V { sin s . sin (8 - α) . sin (s - 6) . sin (s - c)}, and 28 = a + b + e the sum of the sides of the triangle, the radius of whose inscribed circle is R.

Classics.

A.
PLATO.

One of each of the following pair of passages is to be translated, no part being omitted.

Ι.

1. Τούτων τοίνυν ἕνεκα, ὦ Κέβης, οἱ δικαίως φιλομαθεῖς κόσμιοί τ' εἰσὶ καὶ ἀνδρεῖοι, οὐχ ὧν οἱ πολλοὶ ἕνεκά φασιν. ἢ σὺ οἴει; Οὐ δῆτα ἔγωγε. Οὐ γάρ ̓ ἀλλ ̓ οὕτω λογίσσαιτ ̓ ἂν ψυχὴ ἀνδρὸς φιλοσόφου, καὶ οὐκ ἂν οἰηθείη τὴν μὲν φιλοσοφίαν χρῆναι ἑαυτὴν λύειν, λυούσης δὲ ἐκείνης αὐτὴν παραδιδόναι ταῖς ἡδοναῖς καὶ λύπαις ἑαυτὴν πάλιν αὖ ἐγκαταδεῖν καὶ ἀνήνυτον ἔργον πράττειν, Πηνελόπης τινὰ ἐναντίως ἱστὸν μεταχειριζομένης· ἀλλὰ γαλήνην τούτων παρασκευάζουσα, ἐπομένη τῷ λογισμῷ καὶ ἀεὶ ἐν τούτῳ οὖσα, τὸ ἀληθὲς καὶ τὸ θεῖον καὶ τὸ ἀδόξαστον θεωμένη καὶ ὑπ' ἐκείνου τρεφομένη ζῆν τε οἴεται οὕτω δεῖν, ἕως ἂν ζῇ, καὶ ἐπειδὰν τελευτήσῃ, εἰς τὸ ξυγγενὲς καὶ εἰς τὸ τοιοῦτον ἀφικομένη ἀπηλλάχθαι τῶν ἀνθρωπίνων κακῶν. ἐκ δὴ τῆς τοιαύτης τροφῆς οὐδὲν δεινὸν μὴ φοβηθῇ, ταῦτά γε ἐπιτηδεύσασα, ὦ Σιμμία τε καὶ Κέβης, ὅπως μὴ διασπασθεῖσα ἐν τῇ ἀπαλλαγῇ τοῦ σώματος ὑπὸ τῶν ἀνέμων διαφυσηθεῖσα καὶ διαπτομένη οἴχηται καὶ οὐδὲν ἔτι οὐδαμου ᾖ.

2. Εστι δὲ δὴ τὸ κεφάλαιον ὧν ζητεῖς· ἀξιοῖς ἐπιδειχθῆναι ἡμῶν τὴν ψυχὴν ἀνώλεθρόν τε καὶ ἀθάνατον οὖσαν, εἰ φιλόσοφος ἀνὴρ μέλλων ἀποθανεῖσθαι, θαῤῥῶν τε καὶ ἡγούμενος ἀποθανὼν ἐκεῖ εὖ πράξειν διαφερόντως ἢ εἰ ἐν ἄλλῳ βιῳ βιοὺς ἐτελεύτα, μὴ ἀνόητόν τε καὶ ἠλίθιον θάρρος θαῤῥήσει. τὸ δὲ ἀποφαίνειν, ὅτι ἰσχυρόν τί ἐστιν ἡ ψυχὴ καὶ θεοειδές, καὶ ὅτι ἦν ἔτι πρότερον, πρὶν ἡμᾶς ἀνθρώπους γενέσθαι,

οὐδὲν κωλύειν φῂς πάντα ταῦτα μηνύειν ἀθανασίαν μὲν μή, ὅτι δὲ πολυχρόνιόν τέ ἐστι ψυχὴ καὶ ἦν που πρότερον ἀμήχανον ὅσον χρόνον καὶ ᾔδει τε καὶ ἔπραττε πόλλ ̓ ἄττα· ἀλλὰ γὰρ οὐδέν τι μᾶλ λον ἦν ἀθάνατον, ἀλλὰ καὶ αὐτὸ τὸ εἰς ἀνθρώπου σῶμα ἐλθεῖν ἀρχὴ ἦν αὐτῇ ὀλέθρου, ὥσπερ νόσος· καὶ ταλαιπωρουμένη τε δὴ τοῦτον τὸν βίον ζῴη καὶ τελευτῶσά γε ἐν τῷ καλουμένῳ θανάτῳ ἀπολλύοιτο. διαφέρει δὲ δή, φής, οὐδέν, εἴτε ἅπαξ εἰς σῶμα ἔρχεται, εἴτε πολλάκις, πρός γε τὸ ἕκαστον ἡμῶν φοβεῖσθαι· προσήκει γὰρ φοβεῖσθαι, εἰ μὴ ἀνόητος εἴη, τῷ μὴ εἰδότι μηδ' ἔχοντι λόγον διδόναι, ὡς ἀθάνατόν ἐστι. τοιαῦτ ̓ ἅττα ἐστίν, οἶμαι, ὦ Κέβης, ἃ λέγεις· καὶ ἐξεπίτηδες πολλάκις ἀναλαμβάνω, ἵνα μή τι διαφύγῃ ἡμᾶς, εἰ τέ τι βούλει, προσθῇς ἢ ἀφέλης.

II.

1. Οὐ καλῶς, ἔφη, μνημονεύεις, ὦ Σώκρατες, ἃ ἔλεγόν τε καὶ ἀπεκρινόμην σοι. ἔγωγε ἐρωτηθεὶς ὑπὸ σοῦ, εἰ οἱ ἀνδρεῖοι θαῤῥαλέοι εἰσίν, ὡμολόγησα· εἰ δὲ καὶ οἱ θαῤῥαλέοι ἀνδρεῖοι, οὐκ ἠρωτήθην· εἰ γὰρ με τότε ἤρου, εἶπον ἂν, ὅτι οὐ πάντες. τοὺς δὲ ἀνδρείους ὡς οὐ θαῤῥαλέοι εἰσί, τὸ ἐμὸν ὁμολόγημα, οὐδαμοῦ ἐπέδειξας, ὡς οὐκ ὀρθῶς ὡμολογησα. ἔπειτα τοὺς ἐπισταμένους αὐτοὺς ἑαυτῶν θαῤῥαλεωτέρους ὄντας ἀποφαίνεις καὶ μὴ ἐπισταμένων ἄλλων, καὶ ἐν τούτῳ οἴει τὴν ἀνδρείαν καὶ τὴν σοφίαν ταὐτὸν εἶναι. τούτῳ δὲ τῷ τρόπῳ μετιὼν καὶ τὴν ἰσχὺν οἰηθείης ἂν εἶναι σοφίαν. πρῶτον μὲν γὰρ εἰ οὕτω μετιὼν ἔροιό με, εἰ οἱ ἰσχυροὶ δυνατοί εἰσι, φαίην ἄν· ἔπει τα, εἰ οἱ ἐπιστάμενοι παλαίειν δυνατώτεροί εἰσι τῶν μὴ ἐπισταμένων παλαίειν καὶ αὐτοὶ αὐτῶν, ἐπειδὰν μάθωσιν, ἢ πρὶν μαθεῖν, φαίην ἄν· ταῦτα δὲ ἐμοῦ ὁμολογήσαντος, ἐξείη ἄν σοι χρωμένῳ τοῖς αὐτοῖς τεκμηρίοις τούτοις λέγειν, ὡς κατὰ τὴν ἐμὴν ὁμολογίαν ἡ σοφία ἐστὶν ἰσχύς. ἐγὼ δὲ οὐδαμοῦ οὐδ ̓ ἐνταῦθα ὁμολογῶ τοὺς δυνατοὺς ἰσχυ ροὺς εἶναι, τοὺς μέντοι ἰσχυροὺς δυνατούς· οὐ γὰρ ταὐτὸν εἶναι δύναμίν τε καὶ ἰσχύν, ἀλλὰ τὸ μὲν καὶ ἀπὸ ἐπιστήμης γίγνεσθαι, τὴν δύναμιν, καὶ ἀπὸ μανίας τε καὶ ἀπὸ θυμοῦ, ἰσχὺν δὲ ἀπὸ φύσεως καὶ εὐτροφίας τῶν σωμάτων. οὕτω δὲ κἀκεῖ οὐ ταὐτὸν εἶναι θάρσος τε καὶ ἀνδρείαν. ὥστε συμβαίνει τοὺς μὲν ἀνδρείους θαῤῥαλέους εἶναι, μὴ μέντοι τούς γε θαῤῥαλέους ἀνδρείους πάντας· θάρσος μὲν γὰρ καὶ ἀπὸ τέχνης γίγνεται ἀνθρώποις καὶ ἀπὸ θυμοῦ τε καὶ ἀπὸ μανίας, ὥσπερ ἡ δύναμις, ἀνδρεία δὲ ἀπὸ φύσεως καὶ εὐτροφίας τῶν ψυχῶν γίγνεται.

2. ΣΩΚ. Αλλ' εἶχε τοὐτὸν, ὦ φίλε, ἦν, Εὐθύφρου, τὸ θεοφιλὲς καὶ τὸ ὅσιον, εἰ μὲν διὰ τὸ ὅσιον εἶναι, ἐφιλεῖτο τὸ ὅσιον, καὶ διὰ τὸ θεοφιλὲς εἶναι, ἐφιλεῖτο ἂν τὸ θεοφιλές. εἰ δὲ διὰ τὸ φιλεῖσθαι ὑπο θεῶν τὸ Θεοφιλές, θεοφιλὲς ἦν, καὶ τὸ ὅσιον ἂν, διὰ τὸ φιλεῖσθαι, ὅσιον ἦν. νῦν δὲ, ὁρᾶς ὅτι εναντίως ἔχετον, ὡς παντάπασιν ἑτέρω ὄντε ἀλλήλων. τὸ μὲν γὰρ, ὅτι φιλεῖται, ἐστὶν οἷον φιλεῖσθαι· τὸ δ ̓, ὅτι ἐστὶν οἷον φιλεῖσθαι, διὰ τοῦτο φιλεῖται. καὶ κινδυνεύεις, ὦ Εὐθύφρον, ἐρωτώμενος τὸ ὅσιον, ὅ,τι ποτὲ ἐστι τὴν μὲν ουσίαν, μοι αὐτου οὐ βούλεσθαι δηλῶσαι, πάθος δέ τι περὶ αὐτου λέγειν ὅ,τι πέπονθε τοῦτό τὸ ὅσιον, φιλεῖσθαι ὑπὸ πάντων τῶν θεῶν. ὅ,τι δὲ ὄν, ὄυπω εἶπες. εἰ οὖν σοι φίλον, μή με ἀποκρύψη, ἀλλὰ πάλιν εἰπὲ ἐξ ἀρχῆς, τί ποτε ὄν τὸ ὁσίον, εἶτε φιλεῖται ὑπὸ τῶν θεῶν, εἴτε ό,τι δη πάσχει. οὐ γαρ περὶ τούτου διοισόμεθα· ἀλλ ̓ εἰπὲ προθύμως τί ἐστι τό τε ὅσιον καὶ ἀνόσιον. ΕΥΘ. Αλλ' ὦ Σώκρατες, οὐκ ἔχω ἔγωγε ὅπως σοι εἴπω ὃ νοῶ. περιέρ

χεται γάρ πως ἀεὶ ἡμῖν ὃ ἂν ὑποθώμεθα, καὶ οὐκ ἐθέλει μένειν ὅπου ἂν ἱδρυσώμεθα αὐτό. ΣΩΚ. Τοδ ̓ ἡμετέρου προγόνου, ὦ Εὐθύφρον, ἐδικεν εἶναι Δαιδάλου τὰ ὑπο σου λεγόμενα. καὶ εἰ μὲν αὐτὰ ἔλεγον καὶ ἐτιθέμεν, ἴσως ἄν με ἐπέσκωπτες, ὡς ἄρα καὶ ἐμοὶ κατὰ τὴν ἐκεινου συγγένειαν τὰ ἐν τοῖς λόγοις ἔργα ἀποδιδράσκει, καὶ οὐκ ἐθέλει μένειν ὅπου ἄν τις αὐτὰ θῇ. νῦν δὲ (σοὶ γὰρ αἱ ὑποθέσεις ἐισὶν ἄλλου δή τινος δεῖ σκώμματος. οὐ γὰρ ἐθελουσὶ σοι μένειν, ὡς καὶ αὐτῳ σοι δοκεῖ.

B.

PLATO-GRECIAN HISTORY.

1. (a) State the probable years of Plato's birth and death; (b) his original name, and the names of his parents; (c) the number and occasions of his visits to Sicily.

2. How may his hostility to the Sophists of his time be accounted for? What misconceptions have arisen from his use of the word Sophist?

3. State briefly Mr. Grote's view as to the character and position of the Athenian Sophists, and contrast it with the popular opinion on the subject.

4. What reasons are there for supposing that the Platonic Apology is substantially the defence delivered by Socrates on his trial?

5. What were the three counts of the indictment against Socrates? Does the Platonic Apology include a vindication against all of them?

6. In forming our estimate of the conduct of the Athenians towards Socrates, Mr. Grote thinks that there are several extenuating circumstances which should be taken into account?

7. It has been stated that after the death of Socrates the Athenians bitterly repented of their act? There are reasons for doubting whether any such reaction of feeling really took place?

8. Give an account of the number, mode of selection, qualifications, and functions of the Athenian Dicasts.

9. Give a short narrative of the events between the seizure of Phyle by Thrasybulus, and the restoration of the democracy at Athens.

10. What were the causes of the expedition of Cyrus? Trace his march from Sardis to Cunaxa.

11. What was the date of the peace of Callias? Who were the contracting parties? What were its immediate results?

12. What led to the interference of Corinth in the affairs of Sicily B. C. 344? Give a short account of the actions of Timoleon.

13. Draw a map of Sicily, marking on it the positions of Mount Etna, Zancle, Syracuse, Himera, Gela, and Agrigentum.

14. Give some account of the Grecian colonies in Southern Italy.

TO BE TRANSLATED INTO GREEK VERSE.

This is the state of man: to-day he puts forth
The tender leaves of hopes, to-morrow blossoms,
And bears his blushing honours thick upon him:
The third day comes a frost, a killing frost;
And-when he thinks, good easy man, full surely
His greatness is a ripening-nips his root,
And then he falls, as I do. I have ventur'd,
Like little wanton boys that swim on bladders,
This many summers in a sea of glory,

But far beyond my depth: my high-blown pride
At length broke under me; and now has left me,
Weary and old with service, to the mercy
Of a rude stream, that must for ever hide me.
Vain pomp and glory of this world, I hate ye:
I feel my heart new open'd. O! how wretched
Is that poor man, who hangs on princes' favours.
There is, betwixt that smile we would aspire to,
That sweet aspect of princes, and their ruin,
More pangs and fears than wars or women have;
And when he falls, he falls like Lucifer,
Never to hope again.

SHAKSPEARE.

TO BE TRANSLATED INTO LATIN PROSE.

The human mind is of a very imitative nature: nor is it possible for any set of men to converse often together, without acquiring a similitude of manners, and communicating to each other their vices as well as virtues. The propensity to company and society is strong in all rational creatures and the same disposition, which gives us this propensity, makes us enter deeply into each other's sentiments, and causes like passions and inclinations to run, as it were, by contagion, through the whole club or knot of companions. When a number of men are united into one political body, the occasions of their intercourse must be so frequent, for defence, commerce, and government, that, together with the same speech or language, they must acquire a resemblance in their manners, and have a common or national character, as well as a personal one, peculiar to each individual.

Now though nature produces all kinds of temper and understanding in great abundance, it does not follow, that she always produces them in like proportions, and that in every society the ingredients of industry and indolence, valour and cowardice, humanity and brutality, wisdom and folly, will be mixed after the same manner. In the infancy of society, if any of these dispositions be found in greater abundance than the rest, it will naturally prevail in the composition, and give a tincture to the national character.-HUME.

CICERO-ROMAN HISTORY.

A.

Translate into English the entire of one of each pair of the following passages.

I.

1. Stultitiam enim censuerunt, constantia, id est, sanitate vacantem, posse tamen tueri mediocritatem officiorum et vitæ communem cultum atque usitatum. Furorem autem esse rati sunt, mentis ad omnia cæcitatem. Quod quum majus esse videatur, quam insania, tamen ejusmodi est, ut furor in sapientem cadere possit, non possit insania. Sed hæc alia quæstio est. Nos ad propositum revertamur. Cadere, opinor, in sapientem ægritudinem, tibi dixisti videri. A. Et vero ita existimo. M. Humanum id quidem, quod ita existimas. Non enim silice nati sumus. Sed est natura fere in animis tenerum quiddam atque molle, quod ægritudine, quasi tempestate, quatiatur. Nec absurde Crantor ille, qui in nostra Academia vel in primis fuit nobilis, Minime, inquit, assentior iis, qui istam nescio quam indolentiam magnopere laudant: quæ nec potest ulla esse nec debet. Ne ægrotus sim, inquit: sed si fuerim, sensus adsit, sive secetur quid, sive avellatur a corpore. Nam istuc nihil dolere, non sine magna mercede contingit, immanitatis in animo, stuporis in corpore. Sed videamus, ne hæc oratio sit hominum assentantium nostræ imbecillitati, et indulgentium mollitudini: nos autem audeamus non solum ramos amputare miseriarum, sed omnes radicum fibras evellere. Tamen aliquid relinquetur fortasse. Ita sunt altæ stirpes stultitiæ. Sed relinquetur id solum, quod erit necessarium. Illud quidem sic habeto, nisi sanatus animus sit, quod sine philosophia fieri non potest, finem miseriarum nullum fore.

2. Apud majores nostros, justitiæ fruendæ causâ videntur olim bene morati reges constituti. . . . Ergo hoc quidem perspicuum est, eos ad imperandum deligi solitos, quorum de justitia magna esset opinio multitudinis. Adjuncto vero, ut iidem etiam prudentes haberentur, nihil erat, quod homines his auctoribus non posse consequi se arbitrarentur. Omni igitur ratione colenda, et retinenda justitia est; tum ipsa propter sese, nam aliter justitia non esset, tum propter amplificationem honoris et gloriæ. Sed ut pecuniæ non quærenda solum ratio est, sed etiam collocandæ, quæ perpetuos sumptus suppeditet, nec solum necessarios, sed etiam liberales: sic gloria et quærenda et collocanda ratione est. Quanquam præclare Socrates hanc viam ad gloriam proximam, et quasi compendiariam dicebat esse, si quis id ageret, ut, qualis haberi vellet, talis esset. Quod si qui simulatione et inani ostentatione, et ficto non modo sermone, sed etiam vultu, stabilem se gloriam consequi posse rentur, vehementer errant. Vera gloria radices agit, atque etiam propagatur: ficta omnia celeriter, tanquam flosculi, decidunt, nec simulatum potest quidquam esse diuturnum. Testes sunt permulti in utramque partem, sed brevitatis causa familia erimus contenti una. Tiberius enim Gracchus, P. F. tamdiu laudabitur, dum memoria rerum Romanarum manebit. At ejus nec filii vivi probabantur bonis, et mortui numerum obtinent jure

casorum.